Postscript — Eine kleine NASA-Tafel

Most of this stuff we don't need in the Fables but I've stuck it in here to have handy because it is not possible to predict what one might want to know in the course of making an imaginary trip. The metric units here are all OLD metric as contrasted with the new metric units described in the preface.

A NASA website gives the Keplerian attractiveness of the sun as
1.32712440018 × 10^{20}meter^{3}/second^{2}. This
is a shamelessly exquisite degree of precision but presumably one needs that
many digits in order to navigate. This, or the equivalent in "astronomical
units" is what is used for navigation. One does not use the kilogram mass
of the sun, which is to say its inertia, and which is known only to four
decimal places. Although the attractivness is known with exquisite precision
the inertia is known with only mediocre accuracy because G, the ratio of
attractiveness to inertia, is poorly known. G is only known to four or five
places, hardly enough for navigation.

http://ssd.jpl.nasa.gov/astro_constants.html

See the entry for the "heliocentric gravitational constant". I was very glad to see NASA listing the Keplerian attractiveness of the sun in metric units since they are more universal than "astronomical units" and more readily convertible to human-scale Planck units.

At the same site there are some mass ratios. When I say mass in this context
I mean attractiveness instead of inertia because that is how the ratios were
determined — not as ratios of inertias (which we do not know because we do
not push heavenly bodies around to test their inertia) but as ratios of
Keplerian attractivenesses (meter^{3}/second^{2} quantities)
which we tell for individual bodies by observing orbit behavior. The strict
proportionality of inertia to attractiveness is not axiomatic but is something
Dicke and others have attempted to verify. One cannot simply convert these
ratios into inertia-ratios without comment.

Sun/(Earth+Moon) -----328900.56

Earth/Moon-----81.30059

If they were not navigating I would not believe this many digits. It would seem like an inflated claim to precision. But they are placing large bets on the accuracy.

EXACT CONVERSION TO TPM UNITS

Our Planck minutes are defined exactly as 20000/371 seconds and our paces are exactly 200/371 × 2.99792458 meters. (The metric number 299792458 is exact by definition of meter.) So we can make an exact conversion of the NASA "heliocentric gravitational constant" into our TPM units. I will leave off some digits because it would be embarrassing to write them all out.

9.1367857×10^{22} pace^{3}/minute^{2}

NASA says divide by 328900.56 to get the mass of earth and moon. And then it
says multiply that by 81.30059/82.30059 to get earth's. Or else by 1/82.30059
to get the mass of the moon. All that stuff is based on the figure for the sun

Sun: 9.1367857 ×10^{22}
pace^{3}/minute^{2}.

Earth+Moon: 2.77798 ×10^{17}
pace^{3}/minute^{2}.

Earth: 2.74422 ×10^{17} pace^{3}/minute^{2}.

Moon: 3.37540 ×10^{15} pace^{3}/minute^{2}.

NASA data is public domain. Discussion copyright 2002 Leonard
Cottrell.

Table of contents for the Mainstream Physics Fables

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